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Given is a surface embedded in Euclidean 3 space whose Gauss curvature is everywhere positive.
Its metric is <Xu,Xu> = E <Xu,Xv> = F <Xv,Xv> = G for an arbitrary coordinate neighborhood on the surface.
The principal curvatures determine a new metric. In principal coordinates this new metric is
<Xu,Xu> = k1[tex]^{2}[/tex]E <Xu,Xv> = 0 <XvXv> = k2[tex]^{2}[/tex]G
Is this also a metric of positive Gauss curvature?
Its metric is <Xu,Xu> = E <Xu,Xv> = F <Xv,Xv> = G for an arbitrary coordinate neighborhood on the surface.
The principal curvatures determine a new metric. In principal coordinates this new metric is
<Xu,Xu> = k1[tex]^{2}[/tex]E <Xu,Xv> = 0 <XvXv> = k2[tex]^{2}[/tex]G
Is this also a metric of positive Gauss curvature?